Which expression is equivalent to [tex]\((2x^4y)^3\)[/tex]?

A. [tex]\(2x^7y^4\)[/tex]
B. [tex]\(2x^{12}y^3\)[/tex]
C. [tex]\(8x^7y^4\)[/tex]
D. [tex]\(8x^{12}y^3\)[/tex]



Answer :

To determine which expression is equivalent to [tex]\(\left(2 x^4 y\right)^3\)[/tex], we need to carefully apply the rules of exponents.

First, let's expand the given expression [tex]\(\left(2 x^4 y\right)^3\)[/tex]:

1. Expand each component inside the parentheses raised to the power of 3:
[tex]\[ (2 x^4 y)^3 \][/tex]

2. Apply the power of 3 to each individual term inside the parentheses:
[tex]\[ (2)^3 \cdot (x^4)^3 \cdot (y)^3 \][/tex]

3. Calculate each exponent:
[tex]\[ 2^3 \cdot (x^4)^3 \cdot y^3 \][/tex]

- [tex]\(2^3 = 8\)[/tex]
- [tex]\((x^4)^3 = x^{4 \cdot 3} = x^{12}\)[/tex]
- [tex]\(y^3 = y^3\)[/tex]

4. Combine all the components:
[tex]\[ 8 \cdot x^{12} \cdot y^3 \][/tex]

Thus, the fully expanded expression is:
[tex]\[ 8 x^{12} y^3 \][/tex]

So, the expression equivalent to [tex]\(\left(2 x^4 y\right)^3\)[/tex] is:
[tex]\(\boxed{8 x^{12} y^3}\)[/tex]